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Friday, July 10, 2015

Dice bias. A statistics activity

There are so many great reasons to use dice in math class. Strictly speaking, most dice should be non-biased, although students generally don't know what this means or if they do know what it means they don't believe it.

The graph of a die (singular of dice) thrown 100 times should show little bias. If you continue another 900 times and any previously seen bias still occurs one could make a compelling case that the die might be biased. Ask your students what the graph of a die rolled 1000 times should look like.

We played with dice in class. First I had students roll a single die 100 times and then that die was passed to another student who did similarily. Students were asked to keep their results to themselves and they were asked to describe if they thought the die was biased or not. After the whole class' data was brought together the case for the die not being biased was easier to make.

Next had students roll two dice and collect the sums obtained. There is a definite bias int Ensues which will be found. Some sums are more likely and others much less likely (and surprisingly some are impossible, like a sum of 1). We rolled, collected data and graphed results (which forms a wonderful curve that gets lots of attention in statistics classes, but is rarely generated in such classes)

I went out and bought air-dry clay and had students make themselves two six-sided dice. Students were told to make the dice as carefully as possible and they were left to dry (happily they dried sufficiently in 24 hours to make the next part of this possible, though next time I would likely have students paint their dice with clear nail-polish, and let them dry a second night, so they were less likely to crumble... Though this wasn't a big problem for most of the students)

We again did the collecting of sum activity and noticed that our graphs weren't quite so pretty. After collecting 100 rolls from their own dice, students were asked to predict what the sum of rolling the two dice would be given the bias of their handmade dice.

Expected value is one of the harder concepts for students, at least mine. In my class, students themselves came up with the term and a good working definition as well as a reason for the term itself.. Win-Win in my opinion..